I've used this setup many times with my Hitch Climber. It's referred to as an O-rig. If your hitch is a straight peice of cord with no eyes, terminated to the carabiner with knots, the bulk of the knots could potentially interfere with the safe function of the hitch, which is why I got into using it. Also, if your tending slack say from a limb walk, it can be handy. You can use whatever kind of snap you have with a little prussic to fix it wherever you want on the working end of your line.
Actually the problem is with the termination knot on the climbing line, not the hitch cord. That knot can bump up against the hitch which is not a great situation. The line I use most of the time now has a spliced eye which eliminates that problem.